1. Field
The present disclosure relates generally to communications and, more particularly, to coding/decoding schemes for use in communications.
2. Background
The documents listed below are incorporated herein by reference:
[1] S. Lin and D. J. Costello, “Error Control Coding: Fundamentals and Applications”, 1st ed. Prentice Hall, 1983.
[2] G. D. Forney, “Generalized minimum distance decoding,” IEEE Trans. Information Theory, vol. 12, pp. 125-131, April 1996.
[3] D. Chase, “Class of algorithms for decoding block codes with channel measurement information,” IEEE Trans. Information Theory, vol. 18, pp. 170-182, January 1972.
[4] M. P. C. Fossorier and S. Lin, “Soft-decision decoding of linear block codes based on ordered statistics,” IEEE Trans. Information Theory, vol. 41, pp. 1379-1396, September 1995.
[5] R. Koetter and A. Vardy, “Algebraic soft-decision decoding of Reed-Solomon codes,” IEEE Transactions on Information Theory, vol. 49, pp. 2809-2825, November 2003.
[6] A. Vardy and Y. Be'ery, “Bit-level soft-decision decoding of Reed-Solomon codes,” IEEE Trans. Communications, vol. 39, pp. 440-444, March 1991.
[7] J. Jiang and K. R. Narayanan, “Iterative soft-input-soft-output decoding of Reed-Solomon codes by adapting the parity check matrix,” IEEE Trans. Information Theory, vol. 52, no. 8, pp. 3746-3756, August 2006.
[8] J. Jiang, “Advanced Channel Coding Techniques Using Bit-level Soft Information,” Ph.D dissertation, Dept. of ECE, Texas A&M University.
[9] Jason Bellorado, Aleksandar Kavcic, Li Ping, “Soft-Input, Iterative, Reed-Solomon Decoding using Redundant Parity-Check Equations”, Invited paper, IEEE Inform. Theory Workshop (ITW), Lake Tahoe, Calif., USA, Sep. 2-6, 2007
[10] T. J. Richardson, A. Shokrollahi, and R. Urbanke, “Design of capacity-approaching low-density parity-check codes,” IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
[11] D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, pp. 399-431, March 1999.
[12] R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, Mass.: MIT Press, 1963.
[13] M. R. Chari, F. Ling, A. Mantravadi, R. Krishnamoorthi, R. Vijayan, G. K. Walker, and R. Chandhok, “FLO physical layer: An Overview,” IEEE Trans. Broadcast., vol. 53, no. 1, pt. 2, pp. 145-160, March 2007.
FIG. 1 diagrammatically illustrates a prior art coding/decoding scheme for use in a communication system. The arrangement of FIG. 1 uses a concatenated coding structure with turbo coding for an inner code and Reed-Solomon (RS) coding for an outer code. At the transmitter, designated generally at 11, K data source packets are input to an outer RS encoder block 12. The RS encoder 12 takes the block of K input packets and encodes parities to create additional (N-K) parity packets. All the packets output by the RS encoder 12 are byte-level interleaved at 13, and then encoded through an inner turbo encoder 14. All the turbo encoded packets produced by the turbo encoder 14 are bit-level interleaved and modulated (not explicitly shown), and then transmitted through a noisy communication channel shown diagrammatically at 15. The receiver, designated generally at 16, implements the appropriate demodulation and bit-level de-interleaving (not explicitly shown), and includes a turbo decoder 17 that generates log likelihood ratios (LLRs) that respectively correspond to the turbo coded bits that arrive at the turbo decoder 17. The turbo decoder 17 updates the LLR values iteratively until the cyclic redundancy check (CRC) is satisfied or the maximum number of iterations is reached. Hard decisions regarding the bits of successfully decoded packets are de-interleaved at 18. An RS erasure decoder 19 performs erasure decoding to recover the erased packets if possible. All decoded packets are then passed from the RS decoder 19 to an upper layer at 10. The aforementioned documents designated as [1], [13] (and references therein) provide descriptions of the type of coding/decoding scheme shown in FIG. 1.
If (N, K) is the dimension of the RS code being used at the symbol-level (in bytes), then the RS code rate is RRS=K/N. Some prior art systems support multiple code rates so, for example, K=8, 12, 14, or 16 can be used.
The encoding operation of an (N, K) RS code in the aforementioned concatenated coding system (12 in FIG. 1) is illustrated in FIG. 2. Each row in the data block 21 of FIG. 2 represents is a physical layer packet, and each column contains one byte from each of the packets. The first K packets from the top are the systematic packets from the source (see also FIG. 1). The RS encoder acts along each column of data, i.e. it looks at the K systematic bytes in a column and adds (N-K) parity bytes per column. Thus, for an (N, K) code, there would be N physical layer packets at the output of the RS encoder 12 of FIG. 1. The column-wise operation of the RS encoder 12 constitutes an implicit byte interleaving.
Referring again to FIG. 1, at the RS decoder 19, the turbo-decoded physical layer packets belonging to one interleaver block (e.g., the block 21 of FIG. 2) are first stored in a buffer. The CRC of each of the physical layer packets in the buffer is computed to determine whether the packet has been received correctly or not. If the CRC indicates an error, the entire packet is treated as an erasure. Each column of the block is an RS codeword. On the other hand, each row is a single physical layer packet, which is either received correctly or is declared to be an erasure. Thus, each RS codeword in the same RS block contains the same number of erasures in exactly the same positions. This structure can be used to further simplify the erasure decoding algorithm by using a single “generator matrix” to compute the erased locations from K non-erased ones for all the RS codewords. An (N, K) RS code has a redundancy of (N-K) bytes, and is therefore able to correct any combination of (N-K) or fewer erasures within a codeword. However, if more than (N-K) packets in the block are erased, there is no attempt to recover the erased packets in erasure decoding.
It is desirable in view of the foregoing to provide for decoding that is capable of recovering erasures that are lost by the prior art approach.